The purpose of this note is to develop facts about positive real transfer functions for discretetime linear systems, i.e., in the z plane. Positive real functions arise naturally as the impedance functions of passive continuous-time systems.

In this note, given a locally connected topological space X, we characterize those continuous and locally nonconstant real functions on X which are inductively open there. Throughout this note, X denotes a locally connected topological space. Let / be a real function on X. We recall that / is said to be inductively open in X (see [1]) if there exists a set X* Q X such that f{X*) = f(X) and the ...

This paper, which derives some properties of real sewing functions, is divided into three almost independent sections. In the rst, we examine the continuability of uniquely sewing functions. The second section establishes the quasisymmetry of an analytic, strictly increasing function (even at a zero of the derivative) using two diierent techniques. In the third, a new hyperbolicity condition is...

Based on the Turing machine model there are essentially two diierent notions of computable functions over the real numbers. The eeective functions are deened only on computable real numbers and are Type 1 computable with respect to a numbering of the computable real numbers. The eeectively continuous functions may be deened on arbitrary real nunbers. They are exactly those functions which are T...

We define a class, denoted APP, of real-valued functions f : {0, 1}n → [0, 1] such that f can be approximated to within any > 0 by a probabilistic Turing machine running in time poly(n, 1/ ). The class APP can be viewed as a generalization of BPP. We argue that APP is more natural and more important than BPP, and that most results about BPP are better stated as results about APP. We show that A...

We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

practice in sampling, placed Abstract in the context of probability theory. We hope to show the The derivation and correspondence between the two development of weights for approaches to estimation and sample surveys has come almost how for certain classes of exclusively from the sample distributions the two survey tradition. Yet the approaches lead to the same forms of sampling that are result...

Measurement results contain different kinds of uncertainty. Besides systematic errors andrandom errors individual measurement results are also subject to another type of uncertainty,so-called emph{fuzziness}. It turns out that special fuzzy subsets of the set of real numbers $RR$are useful to model fuzziness of measurement results. These fuzzy subsets $x^*$ are called emph{fuzzy numbers}. The m...